Atomic cooling and trapping methods and apparatus

Abstract

An optical trap for laser cooling and trapping atoms without needing a magnetic field. Three pairs of parallel counterpropagating laser beams are directed to cross in a vacuum chamber to form a trapping volume. Rather than having a mutually orthogonal arrangement in which the optical axes of each beam pair forms an angle χ of 45° to a reference axis, z, these angles are instead between 5° ≤ χ ≤ 40° to form a tripod-like arrangement. The beam pairs each have a significant overlap between their counter-propagating beams within the trapping volume which can be defined by the sum of the beam half-widths of the beams of each pair not exceeding twice the beam pair separation distance. Moreover, for good trap formation, at least one of the parallel beam pairs should be sufficiently separated, having a beam half-width sum of at least a quarter of the separation distance.

Description

[0001] Aquark Technologies Ltd - 1 -

[0002] TITLE OF THE INVENTION

[0003] ATOMIC COOLING AND TRAPPING METHODS AND APPARATUS

[0004] BACKGROUND OF THE INVENTION

[0005] The invention relates to the cooling and trapping of atoms with laser light.

[0006] Figures 1 A and 1 B are schematic drawings showing the geometrical arrangement of a standard magneto-optical trap (MOT) for laser cooling and trapping of atoms. Figure 1 A is a perspective view showing the optical axes of three counter-propagating beam pairs, which are arranged mutually orthogonally with their respective optical axes conforming to Cartesian axes x, y, z. Figure 1 B shows a single counterpropagating beam pair, which can be generated by reflecting an input beam back onto its own path with a suitable mirror 10. The optical axes are represented by the superposed solid lines (up and down arrows) and the beam cross-sections are schematically represented by the dotted lines. The optical axes of the three beam pairs intersect at a point, so that the intersecting beam pairs form an intersection or trapping volume V (shown in Figure 1 A schematically with a cube) with a size defined by the respective beam cross-sections of the three beam pairs. MOTs of this kind cool and trap atoms in a two-step process. A magnet is provided to create a magnetic field in the intersection volume. Atoms are cooled in the trapping volume using a two-dimensional (2D) MOT and then in a second step atoms are trapped in the trapping volume using a three-dimensional (3D) MOT in the presence of the magnetic field created by the magnet. For example, Sharma et a / [1] discloses a MOT of this type. Another MOT is described in Lee et a / [5].

[0007] Figures 2A and 2B are schematic drawings showing the geometrical arrangement of an optical trap for laser cooling and trapping of atoms as disclosed in US 2023 / 274849 A1 [2], which does not rely on a magnetic field. Three counterpropagating beam pairs are used but they are in a non-orthogonal alignment. Referring to Figure 2A, if the inclination angle x between each counterpropagating beam pair and a reference axis z were 45 degrees then this would be a mutually orthogonal arrangement of the three beam pairs but instead a non-orthogonal arrangement is used with typical inclination angle values of 25° < x - 40°, more especially 30° < x - 40°, to form a tripod-like arrangement. The three beam pairs are equally spaced radially about the z-axis and so form angles of y = 120° to each other as viewed along the z- axis. The optical axes of a first beam pair are shown with solid lines, a second beam pair with dot-dash lines and a third beam pair with double-dot-dash lines. Moreover, the beams of at least one of the beam pairs are misaligned relative to each other by a small amount, typically 0.5 to 2 degrees, with the misalignment angles labelled a, p, K. Figure 2B shows a single counterpropagating beam pair, which is generated by reflecting an input beam back with a suitable mirror 10, whose mirror plane is tilted slightly away from orthogonal to the optical axis of the input beam, so that a misalignment angle a, p, K is generated between the incident beam and the reflected beam. The optical axes are represented by the solid lines and the beam cross-sections are schematically represented by the dotted lines. This design is capable of cooling and trapping atoms directly from the vapour without the need for a magnetic field and without the need for a two-step process of cooling followed by trapping. An atom cloud is formed in the trapping volume V (shown schematically with a circle). During set-up, the misalignment angles of each beam pair are adjusted to find an optimum for cooling and trapping performance.

[0008] SUMMARY OF THE INVENTION

[0009] According to a first aspect of the disclosure there is provided an optical trap for trapping and cooling atoms, the optical trap comprising: a vacuum chamber operable to provide a vacuum atmosphere in which atoms of an atomic species can be laser cooled via excitation of an electronic transition of the atomic species, referred to as the cooling transition; a laser source configured to generate first to sixth beams of laser light of respective first to sixth beam widths, the beams all having a frequency that is detuned below the frequency of the cooling transition; an optical arrangement configured to direct the first to sixth beams to generate first, second and third counter-propagating beam pairs from the first and second, third and fourth and fifth and sixth beams respectively, such that the first, second and third beam pairs cross each other in a volume of intersection within the vacuum chamber, referred to as the trapping volume, wherein the first, third and fifth beams deviate from a mutually orthogonal arrangement in which they would each form an alignment angle of 45° to a reference axis, such that instead they have respective alignment angles of between 5° and 40° to the reference axis, and wherein the beam axes of the first and second beams that form the first beam pair extend parallel to each other with a deviation from parallel in their mutual alignment of less than 0.1 degrees and are laterally offset from each other by a first beam pair separation distance.

[0010] According to a second aspect of the disclosure there is provided a method of laser cooling and trapping atoms, the method comprising: providing a vacuum chamber operable to provide a vacuum atmosphere in which atoms of an atomic species can be laser cooled via excitation of an electronic transition of the atomic species, referred to as the cooling transition; providing laser light at a frequency detuned below the frequency of the cooling transition; providing first, second and third beams of the laser light with respective first, second and third beam widths; directing the first, second and third beams to propagate across the vacuum chamber along respective first, second and third incident beam paths, wherein the first, second and third incident beam paths deviate from a mutually orthogonal arrangement in which they would each form an alignment angle of 45° to a reference axis, having instead respective alignment angles of between 5° and 40° to the reference axis, and wherein the beam axes of the first and second beams that form the first beam pair extend parallel to each other with a deviation from parallel in their mutual alignment of less than 0.1 degrees and are laterally offset from each other by a first beam pair separation distance. This arrangement differs from that of a conventional MOT in that the respective optical axes of the two beams forming at least one of the beam pairs are not coincident but rather are laterally offset from each other.

[0011] This arrangement has in common with the optical trap of US 2023 / 274849 A1 [2] that there are three counterpropagating beam pairs in a non-orthogonal arrangement and that no magnetic field is needed. However, this arrangement differs from that of the optical trap of US 2023 / 274849 A1 [2] in that the respective optical axes of the two beams forming one or more of the beam pairs are not arranged to cross at the trapping volume. They do not cross at all but rather propagate substantially parallel to each other with a lateral offset. Optimisation of the beam geometry during set-up can be performed by adjusting the separation between the beams of a given beam pair. This has a significant practical advantage, since adjusting the beam separation of any one of the beam pairs does not cause any other changes in the parameter space. This is an advantage compared with US 2023 / 274849 A1 [2] in which optimisation is performed by adjusting the tilt angle between the two beams of a given pair, which makes complex changes in the parameter space and is difficult to achieve without causing the centre of the trapping volume to be displaced.

[0012] In certain embodiments, the first beam pair separation distance is such that the sum of the beam half-widths of the first and second beams is between 0.25 and 2.00 times the first beam pair separation distance in the trapping volume, more particularly with a lower bound of this range of 0.30, 0.35, 0.40, 0.45 or 0.50 combined with an upper bound of this range of any one of 1 .00, 1 .10, 1 .20, 1 .30, 1 .40, 1 .50, 1 .60, 1 .70, 1 .80 or 1 .90.

[0013] Moreover, the beam axes of the third and fourth beams that form the second beam pair may extend parallel to each other with a deviation from parallel in their mutual alignment of less than 0.1 degrees and have a second beam pair separation distance, wherein the sum of the beam half-widths of the third and fourth beams is between 0.25 and 2.00 times the second beam pair separation distance in the trapping volume, more particularly with a lower bound of this range of 0.30, 0.35, 0.40, 0.45 or 0.50 combined with an upper bound of this range of any one of 1 .00, 1.10, 1 .20, 1 .30, 1 .40, 1 .50, 1 .60, 1 .70, 1 .80 or 1 .90.

[0014] In certain embodiments, the second beam pair separation distance is such that the sum of the beam half-widths of the third and fourth beams is between 0.25 and 2.00 times the first beam pair separation distance in the trapping volume, more particularly with a lower bound of this range of 0.30, 0.35, 0.40, 0.45 or 0.50 combined with an upper bound of this range of any one of 1 .00, 1.10, 1 .20, 1 .30, 1 .40, 1 .50, 1 .60, 1 .70, 1 .80 or 1 .90. Moreover, the beam axes of the fifth and sixth beams that form the third beam pair may extend parallel to each other with a deviation from parallel in their mutual alignment of less than 0.1 degrees and have a third beam pair separation distance, and wherein the sum of the beam half-widths of the fifth and sixth beams is between 0.25 and 2.00 times the third beam pair separation distance in the trapping volume, more particularly with a lower bound of this range of 0.30, 0.35, 0.40, 0.45 or 0.50 combined with an upper bound of this range of any one of 1 .00, 1.10, 1 .20, 1 .30, 1 .40, 1 .50, 1.60, 1.70, 1.80 or 1.90.

[0015] Further, the third beam pair separation distance may be such that the sum of the beam halfwidths of the fifth and sixth beams is between 0.25 and 2.00 times the first beam pair separation distance in the trapping volume, more particularly with a lower bound of this range of 0.30, 0.35, 0.40, 0.45 or 0.50 combined with an upper bound of this range of any one of 1 .00, 1.10, 1 .20, 1 .30, 1 .40, 1 .50, 1 .60, 1 .70, 1 .80 or 1 .90.

[0016] While in the context of the present invention we have defined substantially parallel in the context of the beams of a beam pair to mean a deviation from parallel in the mutual alignment of the beam axes of the two beams of less than 0.1 degrees alternative definitions could take a different value such as 0.05 degrees or 0.01 degrees.

[0017] In summary, at least one of the beam pairs is configured with parallel beams having a significant lateral offset. The other beam pairs may also have their beams parallel but their beam separation distance could either be substantially zero or significant. For all beam pairs however, their separation distance in the trapping volume should not be too large as specified in relation to the beam overlap between the two beams that make up a beam pair, with this being defined in terms of the ratio between beam half-width and the separation distance. For each counter-propagating beam pair the two beam widths and the separation distance between the two beams are jointly configured to ensure that in the volume of intersection there is significant overlap between the two beams. Beam width and half-width are defined as the 1 / e2 value and will be a beam diameter or radius in the case of a beam of circular cross-section or two values for the major and minor axes in the case of a beam of elliptical cross-section. More specifically, the separation distance of any given beam pair can be selected such that the sum of the beam half-widths of the two beams forming the beam pair is below 2.00 times the separation distance in the trapping volume with at least one of the beam pairs have the sum of the beam half-widths being at least 0.25 times the separation distance.

[0018] It is also possible in some embodiments for one or more of the other beam pairs to be nonparallel, i.e., tilted or misaligned relative to each other by a small angular amount of 0.5 to 2 degrees as described in US 2023 / 274849 A1 [2] such that the beams of the misaligned beam pair cross in the trapping volume and more specifically satisfy the criterion that the sum of their beam half-widths is between 0.25 and 2.00 their separation distance in the trapping volume. This hybrid design between the present invention and US 2023 / 274849 A1 [2] would therefore have at least one beam pair with non-coaxial parallel beams according to the present invention and at least one beam pair that are misaligned according to US 2023 / 274849 A1 [2], There are multiple options for generating and suitably directing the cooling beams. For example, the cooling laser source may consist of one laser, whose output beam is split to generate the first to third beams. The cooling laser source may alternatively consists of three lasers, each generating one of the first to third beams, First, second and third reflector arrangements may be provided, these being arranged to reflect the first, second and third beams after they have propagated across the vacuum chamber so that they propagate back across the vacuum chamber as the fourth, fifth and sixth beams respectively. The laser source may also consist of six lasers, each generating one of the first to sixth beams, in which case reflectors are not needed.

[0019] Polarising components may be arranged to provide the first to sixth beams with respective defined polarisation states when they enter the vacuum chamber.

[0020] In certain embodiments, the laser source consists of one laser, whose output beam is split to generate the first, third and fifth beams and wherein the second, fourth and sixth beams are derived from the first, third and fifth beams respectively. In certain other embodiments, the laser source consists of first to third lasers to generate the first, third and fifth beams respectively and wherein the second, fourth and sixth beams are derived from the first, third and fifth beams respectively.

[0021] With either of these two laser source configurations, the second beam can be derived from the first beam by arranging a first beam splitter cube to receive and reflect the first beam as received after its traversal of the vacuum chamber and providing a first mirror combination to re-route the beam reflected by the first beam splitter cube to pass it again through the beam splitter cube in a counter-propagating direction in relation to the first beam with a lateral offset between the beam axes of the first and second beams to provide the first beam pair separation distance. Further, the fourth beam can be derived from the third beam by arranging a second beam splitter cube to receive and reflect the third beam as received after its traversal of the vacuum chamber and providing a second mirror combination to re-route the beam reflected by the second beam splitter cube to pass it again through the beam splitter cube in a counterpropagating direction in relation to the third beam with a lateral offset between the beam axes of the third and fourth beams to provide the second beam pair separation distance. Still further, the sixth beam can be derived from the fifth beam by arranging a third beam splitter cube to receive and reflect the fifth beam as received after its traversal of the vacuum chamber and providing a third mirror combination to re-route the beam reflected by the third beam splitter cube to pass it again through the third beam splitter cube in a counter-propagating direction in relation to the fifth beam with a lateral offset between the beam axes of the fifth and sixth beams to provide the third beam pair separation distance. Adjusters such as linear translation stages may be used to adjust the beam pair separation distance of any given beam pair. Namely, a first adjuster can be provided that is actuatable to vary the first beam pair separation distance, a second adjuster can be provided that is actuatable to vary the second beam pair separation distance, and / or a third adjuster can be provided that is actuatable to vary the third beam pair separation distance.

[0022] An advantage of having any given beam pair made up of essentially parallel beams is that it is possible to adjust the separation between those beams using a suitable adjuster, such as a single axis positioner to translate a mirror or a laser source, without changing any other parameter that is relevant for the trap. This gives improved adjustment control of the trap compared with the situation of misaligned beams where an adjustment of the tilt angle will tend to simultaneously change the amount of beam overlap in the trapping volume.

[0023] With the above-described approach it is possible to provide an all-optical trap, i.e. one that does not rely on the presence of a magnetic field. Since no magnetic field is used for the cooling effect exploited by the present invention, of course a corresponding optical trap does not require any magnetic coils or any other form of magnetic field generator to be provided, since no magnetic field needs to be generated in the vacuum chamber. A Zeeman slower is also not needed.

[0024] An optical trap embodying the invention does not need to include a magnetic field generator, since laser cooling takes place without a magnetic field being present.

[0025] While no magnetic field, more precisely no quadrupole magnetic field, is required for cooling and trapping as in a conventional MOT, the above-described approach can function in the presence of a magnetic field. In particular, we have demonstrated experimentally that our trap still works in the presence of uniform magnetic fields of up to 5 Gauss. In addition to the system working in a uniform magnetic field, while we have shown that a quadrupole magnetic field is not required for cooling and trapping, the apparatus could additionally be provided with a suitable quadrupole magnet if the option of a mode of operation as a conventional magnetooptical trap was for some reason desired.

[0026] In certain embodiments, the first, second and third alignment angles are equal to each other. In other embodiments, at least two of the first, second and third alignment angles are different from each other.

[0027] The first, second and third reflector arrangments may be configured such that the reference axis and each pair of incident and reflected beam paths lie at least approximately in a common plane, thereby defining first, second and third such planes. The first, second and third planes may be approximately equally angularly spaced as viewed along the reference axis. In certain embodiments, polarising components are arranged to provide the first, second and third beams with respective defined polarisation states when they enter the vacuum chamber. The first, second and third reflector arrangements may be configured to ensure that the defined polarisation states of the first, second and third beams are preserved on reflection, e.g. circular polarisation or linear polarisation.

[0028] For certain atomic species, there is a further electronic transition, referred to as the repump transition, which is required to be excited for efficient cooling to occur. In such cases, the laser source or a further laser source is configured to generate further laser light at a further frequency tuned at the frequency of the repump transition. The optical arrangement may then further comprise a beam combiner operable to combine the laser light and the further laser light so that each of the first, second and third beams contain both the laser light and the further laser light.

[0029] Preferably, the beams are at least approximately collimated as they cross the vacuum chamber. Approximate collimation may be characterised by the beam divergence, where a beam divergence 0 = 0 corresponding to a collimated beam, and approximate collimation as concerns the present invention may be a beam divergence, 0, less than or equal to one of 1 , 2, 3, 4, 5, 6, 7, 8, 9 or 10 degrees.

[0030] In principal embodiments, the first, second and third alignment angles form an angle of between 25° and 40° to the reference axis, more especially between 30° and 40°.

[0031] In certain embodiments, the atomic species has a further electronic transition, referred to as the repump transition, which is required to be excited for efficient cooling to occur. The above- mentioned laser source or a further laser source is then configured to generate further laser light at a further frequency tuned at the frequency of the repump transition. A beam combiner may then be provided which is operable to combine the laser light and the further laser light so that each of the first to sixth beams contain both the laser light and the further laser light.

[0032] The first to sixth beams may be at least approximately collimated as they cross the vacuum chamber. Approximate collimation may be characterised by the beam divergence, where a beam divergence 0 = 0 corresponding to a collimated beam, and approximate collimation as concerns the present invention may be a beam divergence, 0, less than or equal to one of 1 , 2, 3, 4, 5, 6, 7, 8, 9 or 10 degrees.

[0033] The optical trap according to the above designs does not need a magnetic field generator.

[0034] The first, second and third alignment angles may be between 20° and 40°, more especially 25' and 40°. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] This invention will now be further described, by way of example only, with reference to the accompanying drawings.

[0036] Figures 1 A and 1 B are schematic drawings showing the geometrical arrangement of a known magneto-optical trap (MOT) according to Sharma et a / [1].

[0037] Figures 2A and 2B are schematic drawings showing the geometrical arrangement of a known optical trap according to US 2023 / 274849 A1 [2],

[0038] Figures 3A, 3B and 3C are schematic drawings showing the geometrical arrangement of an optical trap according to a first embodiment.

[0039] Figure 4 is a schematic drawing showing the geometrical arrangement of an optical trap according to a second embodiment.

[0040] Figure 5 is a schematic drawing showing the geometrical arrangement of an optical trap according to a third embodiment.

[0041] Figure 6 is a schematic drawing showing the geometrical arrangement of an optical trap according to a fourth embodiment.

[0042] Figure 7A is a schematic drawing of a beam return subassembly for circularly polarised counterpropagating beam pairs using a polarising beam splitter cube.

[0043] Figure 7B is a schematic drawing of a beam return subassembly for linearly polarised counterpropagating beam pairs using a polarising beam splitter cube.

[0044] Figure 7C is a schematic drawing of a beam return subassembly using a replicated lateral transfer retroreflector mirror.

[0045] Figure 8 shows an optical setup for providing a stabilised cooling laser beam.

[0046] Figure 9 shows an optical setup for providing a stabilised repump laser beam.

[0047] Figure 10 shows a setup for the optical trap.

[0048] Figure 11 is a schematic drawing of a first variant of the first embodiment.

[0049] Figure 12 is a schematic drawing of a second variant of the first embodiment.

[0050] Figure 13 is a schematic drawing of a third variant of the first embodiment. DETAILED DESCRIPTION

[0051] In the following the invention is described by way of example for cooling85Rb atoms. The invention is usable for any atomic species that is capable of being optically cooled. In principle any atoms from Group I or II of the periodic table are amenable to optical cooling. Moreover, atoms of other groups may be used, for example Ytterbium. In practice to date, atomic species for which optical cooling has been demonstrated include: Rb, Cs, Li, Sr, Ca, K, Fr and Yb. In the case of Sr, it is further noted that a repump is not needed, so the corresponding equipment described below in connection with repump would be omitted.

[0052] Figures 3A, 3B and 3C are schematic drawings showing the geometrical arrangement of an optical trap for laser cooling and trapping of atoms according to a first embodiment. The optical trap does not rely on use a magnetic field. Three counterpropagating beam pairs, each comprising a polarised input beam and a reflected beam, are used in a non-orthogonal alignment. Referring to Figure 3A, if the inclination angle x between each counterpropagating beam pair and a reference axis z were 45 degrees then this would be a mutually orthogonal arrangement of the three beam pairs but instead a non-orthogonal arrangement is used with typical inclination angle values of 25° < x - 40° and a range of 5° < x - 40° being possible. By way of example, the inclination angle, x, shown in Figure 3A is approximately 30°.

[0053] A tripod-like arrangement of the optical axes of the three beam pairs is therefore formed. The three beam pairs are equally spaced radially about the z-axis and so form angles of y = 120° to each other as viewed along the z-axis. The optical axes of the three beam pairs are shown with solid lines and extend parallel to each other separated by respective distances a, b, c. Figure 3B shows a single counterpropagating beam pair, which is generated by reflecting an input beam back as a reflected beam with a suitable pair of mirrors 12, 14, whose mirror planes are each tilted at 45 degrees from the optical axes of the input and output beams (or other angle combination that sums to 90 degrees), to reflect the input beam with a separation distance x, where % is a generic label for ‘a’, ‘b’ or ‘c’. The intensity profiles of the beam cross-sections are schematically represented by the dotted lines. Figure 3C is a schematic graph of the intensity, I , of a single beam, where the beam half-width, r, can be taken as the 1 / e2reduction of beam intensity from its maximum value at the optical axis, O, which is about 13.5% of the maximum. This design is capable of cooling and trapping atoms directly from the vapour without the need for a magnetic field and without the need for a two-step process of cooling followed by trapping. An atom cloud is formed in the intersection or trapping volume l / (shown schematically with a circle) directly from vapour and without a magnetic field. During set-up, the separation distances a, b, c of each beam pair can be adjusted to find an optimum for cooling and trapping performance. With two mirrors tilted at 45 degrees, the adjustment of separation distance can take place by linear translation of one of the mirrors 12, 14 in a direction orthogonal to the optical axes of the input and reflected beams, the direction lying in a plane formed by the input and reflected beam optical axes, as indicated schematically by the double-headed arrow. This may be achieved by mounting one of the mirrors 12, 14 on a linear translation stage 32.

[0054] While the optical axes of the beams of each beam pair are shown as being parallel to each other, a deviation from parallel in their mutual alignment may be tolerated, for example a deviation of less than 0.1 degrees.

[0055] While the optical axes of the beam pairs are shown equally spaced radially about the z-axis, i.e., at angles y = 120° to each other as viewed along the z-axis, deviations from equal radial spacing may be used. For example, deviations from a radial spacing of y = 120° may be possible, e.g. by up to ±1°, ±2°, ±3°, ±4°, ±5°, ±6°, ±7°, ±8°, ±9°, ±10°. The three incident beam paths are aligned at an inclination angle x away from the z-axis. A common inclination angle is shown with a value of x = 30°, but in other embodiments unequal inclination angles could be used. Each incident beam path thus lies in a plane containing the z-axis and forms an inclination angle x to the z-axis. Each of these three planes subtends an angle of 120° to the other two planes to provide equal angular spacing of the three beams. In the following description, the laser beams are assumed to be collimated. In practice, collimated, or at least only weakly diverging or converging beams, will be used. Each beam is reflected back from its incident beam path into a reflected beam path, the reflections taking place in the plane of the lower circle. Each reflection is performed so as to maintain the polarisation state of the beam, which may be circular or linear. Preservation of circular polarisation may be achieved by a quarter waveplate and dielectric mirror combination. The three reflected beam optical axes (lines with arrows pointing up) are separated by respective separation distances (a, b, c) from the incident beam optical axes. The displacement of the optical axis of the reflected beam relative to that of the incident beam is shown in each case to be away from the z-axis but could equally well be towards the z-axis. The optical axis of each reflected beam lies in the same above-mentioned plane as that of its incident beam and lies at the same angle of inclination relative to the z-axis. The separation distances (a, b, c) may in general be different from each other, but they could be all the same, or two of them could be the same. The separation distances (a, b, c) and the finite beam cross-sections result in a volume of intersection, V, being formed which is the volume traversed by the beams both along their incident beam paths and along their reflected beam paths. The six beam components interfere with each other in the volume of beam intersection. This interference is what causes the cooled atom cloud to be formed in the volume of intersection.

[0056] For efficient operation of an optical trap according to embodiments of the invention, it is considered to be necessary that all the beams are at least approximately collimated and that the beam diameters, inclination angles and separation distances are chosen collectively such that all six beam components cross in a common region (the volume of beam intersection).

[0057] The magnitude of the beam separation distance x of any given beam pair is selected to be similar to the sum of the beam half-widths, i.e. radii for circular cross-section beams, rltr2of the two beams making up the beam pair. More specifically, for at least one of the beam pairs, the sum of the beam half-widths, r, of the incident and reflected beams may be in the range between 0.25 and 2.00 times the beam pair separation distance, x , i.e.: r. + r20.25 < - - - < 2.00 x where it will be understood that the relevant values for the beam diameters and the separation distance are where the beams traverse the trapping volume. While at least one of the beam pairs must satisfy this range criterion, the other beam pairs need only satisfy the upper bound of the range and may have a smaller separation distance that the specified range.

[0058] As a quantified example of satisfying this range criterion, if the beam half-widths of the incident and reflected beams are both 5 mm, then the beam separation can be in the range

[0059] 5 mm to 40 mm. Generally, the range of useable separation distances depends on beam halfwidth, with larger beam radii allowing larger separation distances. The beam half-width is defined by the 1 / e2 reduction of beam intensity from its maximum value along a line lying in a plane orthogonal to the beam axis and extending in a direction to a point where the plane intersects the beam axis of the beam with which it forms a pair. The 1 / e2value can be determined from a Gaussian fit for a beam with a Gaussian function cross-section.

[0060] Alternatively, a Bessel fit may be used in the case of a beam with a Bessel function crosssection. It will be understood that if the beams of a pair are exactly parallel and the beams are perfectly collimated then the beam overlap as defined in the above equation by the ratio (rx+ r^- / x will be constant along the length of the beam pair. However, any slight misalignment of the beams from parallel and any beam divergence will result in the beam overlap varying along the length of the beam pair, in which case it is the value of beam overlap in the trapping volume that is relevant.

[0061] It is noted that the beam half-widths of the two beams of any given pair need not have the same size, i.e., may have different magnitudes.

[0062] With the arrangement of parallel counterpropagating beam pairs, it is experimentally straightforward to adjust beam separation of each beam pair in a stepwise or continuous manner, for example, each separation distance in turn. Another relevant parameter to optimise is the cooling detuning level. Optimisation is performed to improve the cloud formation, e.g. in terms of its temperature, shape or density, and hence find an optimum parameter combination for forming a dense, cold and approximately spherically shaped cloud. It is expected that the optical trap's performance is comparable to that of a conventional MOT in terms of atom numbers (~18), cloud density (1011atoms / cm3) and cloud temperature (< 50 pK). The atom cloud formed at the volume of beam intersection is typically millimetre-sized and has a somewhat elongate (roughly ellipsoid) shape with the long axis of the ellipse aligned along the optical axes of one of the beam pairs. The cloud shape and cloud volume can be manipulated experimentally by incrementally adjusting the magnitude of one or more of the separation distances (a, b, c). This effect can be exploited to find an optimum combination of separation distances by incrementally reducing both the size of the cloud and its aspect ratio, so as to form a small, dense cloud with a near-spherical shape, as is usually desired.

[0063] Figure 4 is a schematic drawing showing the geometrical arrangement of an optical trap according to a second embodiment. The second embodiment differs from the first embodiment only in that the second and third beam pairs counter-propagate in a coaxial manner, i.e., there is zero separation distance between the beam axes of these beam pairs (a<>0, b=0, c=0), i.e., only the first beam pair satisfies the equation: r. + r2

[0064] 0.25 < - - - < 2.00 x whereas for the second and third beam pairs: r. + r2

[0065] - - - « 0 x

[0066] In a further embodiment (not illustrated) the first and second beam pairs could be laterally offset in the range 0.25 to 2.00 as specified above and the third beam pair could be made of coaxial counter-propagating beams.

[0067] Figure 5 is a schematic drawing showing the geometrical arrangement of an optical trap according to a third embodiment. The third embodiment has the same arrangement of three beam pairs as in the first embodiment but is additionally provided with a fourth beam pair. The fourth beam pair is made up of parallel, laterally offset beams with a beam axis separation distance that is labelled ‘d. The beam axes of the fourth beam pair extend along the reference axis, ‘z’.

[0068] Figure 6 is a schematic drawing showing the geometrical arrangement of an optical trap according to a fourth embodiment. The fourth embodiment has the same arrangement of three beam pairs as in the second embodiment but is additionally provided with fourth and fifth beam pairs which are shown as counter-propagating in a coaxial manner, i.e., there is zero separation distance between the beam axes of these beam pairs (a<>0, b=0, c=0, d=0, e=0), A variant would be to have non-zero separation distance between any of the beam pairs b to e. Figure 7A is a schematic drawing of a beam return subassembly 16 for circularly polarised counterpropagating beam pairs based around a polarising beam splitter (PBS) cube 20. The incident beam passes through a quarter waveplate 22, through the PBS cube 20 and then a halfwave plate 24 before being reflected by multiple mirrors M1 , M2, M3 with reference numerals 26, 28, 30 to arrive back at the PBS cube 20 on a path that is orthogonal to the path of the incident beam and such that the beam is reflected by the PBS cube 20 back along the path of the incident beam but laterally displaced therefrom by a separation distance, x, the return beam then passing through the quarterwave plate 22. The optical axis of the return beam is thus laterally offset from that of the input beam by a separation distance, x, so that the input and return beams counterpropagate and are parallel to each other. This design using a PBS cube allows a high degree of control over the beams and their polarisation states. The separation distance between the input and return beams can be made adjustable by commonly mounting the mirrors M2 and M3 on a linear translation stage 32 with a motion axis in the direction indicated by the double-headed arrows, i.e., in the plane formed by the input and return beams and orthogonal to the propagation direction of the input and return beams.

[0069] Figure 7B is a schematic drawing of a beam return subassembly 16 for linearly polarised counterpropagating beam pairs based around a PBS cube 20. The overall setup is similar to that of Figure 7A, differing only in that the quarterwave plate 22 of Figure 7A is exchanged for a halfwave plate 22’.

[0070] Figure 7C is a schematic drawing of a beam return subassembly using a replicated lateral transfer retroreflector mirror, which is commercially available from Thorlabs, Inc. with product number HHR19385-M03. The replicated lateral transfer retroreflector mirror 34 has three orthogonal surfaces to reflect light with a lateral displacement of beam position, with the reflected beam being parallel to the incident beam. The beam separation, x, between the incident and reflected beams is adjustable by lateral displacement of the mirror to change the distance between the optical axis of the incident beam and the vertex where the three orthogonal surfaces meet. The separation distance between the input and return beams can be made adjustable by mounting the replicated lateral transfer retroreflector mirror 34 on a linear translation stage 32 with a motion axis in the direction indicated by the double-headed arrows, i.e., in the plane formed by the input and return beams and orthogonal to the propagation direction of the input and return beams so that motion provided by the linear translation stage varies the distance between the optical axis of the incident beam and the above-mentioned vertex point.

[0071] Figures 8 to 10 are schematic drawings showing various parts of a system used to demonstrate optical trap operation experimentally with a vapour of85Rb atoms. Figures 8 and 9 show optical setups for providing stabilised cooling and repump laser beams respectively. It is noted that both these stabilisation schemes are known, and also that the skilled person knows of other stabilisation schemes that would be suitable. Figure 10 shows the system setup around the optical trap's vacuum chamber.

[0072] With reference to Figure 8, the cooling setup 100 is based on a laser source 102, which is a distributed feedback diode (DFB) laser. The DFB has a centre wavelength of 780 nm, linewidth of ~0.6 MHz and output power range 20-80 mW. The cooling laser is stabilised to the85Rb transition: using modulated transfer spectroscopy [3]. The beam from the cooling laser 102 is initially passed through an optical isolator 104 and half-wave plate 106. A polarising beam splitter (PBS) 108 is arranged in the beam to divide it into two branches. One branch, having a small fraction of the beam power, is used as input to control a laser stabilisation system (vertical branch), whilst the remainder of the optical power, referred to as the main beam, ultimately provides the incident beams to the trap (straight-through branch). The stabilisation branch is supplied via a mirror 118 to a further PBS 120 which again divides the beam into two. The straight-through branch from the PBS 120 leads directly to a vapour cell 122 and forms the probe beam of a pump-probe scheme, the probe beam having the frequency of the laser 102. The probe beam thus traverses the vapour cell 122 from right-to-left in the drawing. The branch deflected from the PBS 120 is used to generate the pump beam. The pump beam branch is directed by further mirrors 138 and 140 to an acousto-optical modulator (AOM) 142. The AOM 142 diffracts the input beam to output zeroth and two first order diffraction beams. These three beams are reflected back from a mirror 148 and on their passage back through the AOM 142 are recombined into a single beam. A quarter-wave plate 146 is arranged between the AOM 142 and the mirror 148 to provide the desired circular polarisation. The combined, reflected beam passes via mirrors 140 and 138, straight-through passage through the PBS 120, further routing with mirrors 126 and 130 and a further PBS 124, as well as via passage through a halfwave plate 128, to traverse the vapour cell 122 as the pump beam from left-to-right in the drawing, i.e. in the opposite direction to the probe beam. These components thus collectively form a saturated absorption spectroscopy arrangement to generate an error signal from four- wave mixing in the rubidium atoms contained in the vapour cell. In the vapour cell, each of the pump and probe beams traversing the vapour cell 122 generates a sub-Doppler spectrum, slightly shifted in frequency relative to the other. By subtracting the resultant spectra, an error signal is generated from the photodiode output. The first order diffracted beam used for the laser stabilisation is composed of the main carrier of frequency wc = wo + COAOM with sidebands of frequency cos = ± comod- The double-pass through the AOM 142 further modulates the main carrier beam, which now has a frequency of co = wo + 2COAOM with sidebands offset by ±comod- In the experimental set-up, the pump beam has a frequency shift of wShift = 160 MHz with an additional modulation of com0d = 2TT X 0.3 MHz. Considering that the atoms move inside the vapour cell with velocity v, they interact with the probe beam at the frequency of coPr0be = wo - kv. In the case of the pump beam, the atoms interact at a frequency of copump = co0+ 2COAOM + kv, where ±k are the pump and probe beams wavevectors. A spectrum is generated only when the atoms resonate with both beams simultaneously. Therefore, the only atoms that interact are those that are travelling towards the probe beam with a velocity of v = COAOM / k. Since the error signal is generated from two sidebands of the first order diffracted beam, the feedback from the error signal will stabilise the laser 102 at an output frequency of coo + COAOM, i.e. shifted by COAOM from what is required. In order to reverse this shift, a further AOM 110 is arranged in the path of the main laser beam. The first order diffraction beam output from the AOM 1 10 at frequency coo is then supplied via mirrors 112 and 1 14 to an optical fibre coupler 1 16 to couple the light into an optical fibre 117, which is used for convenient delivery of the cooling laser beam to the trap. The amount of laser detuning, 5, below the resonant frequency (i.e. so-called red detuning), in this case from the85Rb cooling transition, is conveniently represented in units of F, where F = 2TT x 6 MHz is the natural decay rate of85Rb. For the example system, the detuning 5 = -1 ,5F. The error signal is extracted from the left-hand-side output of the vapour cell 122 via a PBS 24 (straight-through path), focusing lens 132 and photodiode 134. The electrical signal output from the photodiode 134 is then amplified and demodulated with suitable demodulation electronics 136 to generate the error signal. The error signal is then fed back in a feedback loop via a proportional-integral-derivative (PID) controller to control the laser 102 by adding the error signal as a modulation to the laser's drive signal.

[0073] With reference to Figure 9, the repump laser set up 200 is based on a laser source 202, which is matched to form a pair with the cooling laser source 102, i.e. in this example being another DFB with the same specifications. The repump laser is stabilised to the following85Rb transition: using carrier modulation spectroscopy [4], The repump laser 202 is stabilised using a similar approach to the cooling laser, but without the need for dedicated demodulation electronics for demodulating the signal [4], The repump laser beam is passed through an optical isolator 204 and a half-wave plate 206. Then a PBS 208 is used to separate the repump laser beam in two. One beam, having a small fraction of the beam power, is used as input to control a laser stabilisation system (vertical branch), whilst the remainder of the optical power, referred to as the main beam, ultimately provides the incident beams of the trap (straight-through branch). The branch for laser stabilisation is supplied via a mirror 218 to an AOM 242, the AOM 242 having an additional modulation applied on top of its native frequency, as described above in the cooling laser stabilisation set-up. The modulation added to the AOM 242 is in the form of a square wave of frequency com0d = 1 MHz. This causes the first order diffracted beam from the AOM to split into two components of frequencies coi = coo + COAOM + comod and C02 = coo + COAOM - comod which respectively form pump and probe beams for a saturated absorption spectroscopy arrangement based around a vapour cell 222 containing Rb vapour. The probe beam passes through the PBS 220 and traverses the vapour cell 222 from left-to- right in the drawing. The pump beam is routed via deflection by the PBS 220 and suitable mirrors 226 and 230 as well as passage through a half-wave plate 228 and finally deflection by a further PBS 224 to traverse the vapour cell 222 from right-to-left in the drawing, i.e. in the opposite direction to the probe beam. The probe beam output from the vapour cell 222 via the straight-through branch of the PBS 224 is focused by a lens 232 onto a quadrant photodiode 234. (As an alternative to a quadrant photodiode 234 a balanced photodiode or two separate photodiodes could be used.) The error signal is obtained from the probe beam output of the vapour cell 222 via a PBS 224 (straight-through path), focusing lens 232 and photodiode 234. In the vapour cell, each of the pump and probe beams traversing the vapour cell 222 generates a sub-Doppler spectrum, slightly shifted in frequency relative to the other. By subtracting the resultant spectra, an error signal can be generated from the photodiode segment outputs. The error signal is then fed back in a feedback loop via a proportional-integral-derivative (PID) controller to control the laser 202 by adding it as a modulation to the laser's drive signal. Since the error signal is generated from two sidebands of the first order diffracted beam, the feedback from the error signal will stabilise the repump laser at an output frequency of w0+ COAOM, i.e. shifted by COAOM from what is required. In order to reverse this shift, a further AOM 210 is arranged in the path of the main laser beam, similar to the cooling laser stabilisation system. The first order diffraction beam output from the AOM 210 at frequency coo is then supplied via mirrors 212 and 214 to an optical fibre coupler 216 which couples the beam into an optical fibre 217, which is used for convenient delivery of the repump laser beam to the trap. An advantage of this repump stabilisation system is that it does not require complicated electronics and so is suited to portable, low-power systems.

[0074] The above-described detuning of the cooling and repump lasers from resonance is achieved using AOMs. An alternative would be to use a scheme based on a single laser source and then the laser beam could be used to generate both the cooling and repump beams with an electrooptic modulator (EOM). An EOM is a device which modulates the phase of a beam by driving a low frequency electric field across a crystal that exhibits in response a linear shift of its refractive index. After stabilisation as described above with reference to Figure 8 and Figure 8, the cooling and repump beams are combined into a single beam and delivered to the optical trap in the beam geometry shown in Figure 10.

[0075] Figure 10 shows an experimental setup for the optical trap 300. The cooling and repump beams are delivered to the optical trap setup 300 via the respective optical fibres 117, 217. The cooling and repump beams are first combined with a 2-to- 1 fibre coupler 301 . A power ratio of 3:1 between the cooling and repump beams is suitable. The combined cooling and repump beams are split into three components of equal power by a 1 -to-3 fibre splitter 302. The respective output sides of the splitter 302 are three sections of optical fibre 304, 306, 308. These combining and splitting functions can be achieved in optical fibre using appropriate combiners and splitters taking care to preserve polarisation as desired, e.g. using nonpolarising or polarisation preserving combiners, splitters and fibre. Alternatively, free-space optical components could be used for the combining and splitting. The optical fibres 304, 306, 308 terminate in respective optical fibre couplers 310, 312, 314 which are arranged to provide the beam geometries for the incident beam paths as described in the specific embodiments.

[0076] The three beams output from the respective optical fibre couplers 310, 312, 314 have an approximate Gaussian power distribution in cross-section and are each collimated with a collimator lens (not separately shown) to a diameter of 5.4 mm, where the diameter is taken as the 1 / e2value. The light polarisation state in the three beams output from the optical fibres 310, 312, 314 is set to circular using respective PBSs 316, 318, 320 and quarter waveplates 322, 324, 326. The three beams then traverse a vacuum chamber 350 which has windows that are transparent to the wavelengths of the beams or is entirely made of transparent material, e.g. a suitable glass. After traversing the vacuum chamber 350 each beam is reflected by a quarter waveplate and mirror combination 328 / 334, 330 / 336, 332 / 338 so that the reflected beam is parallel to but laterally offset from the incident beam, the optical axes of the parallel incident and reflected beams being characterised by a separation distance. After reflection, the reflected beams then traverse the vacuum chamber 350, so that each beam pair is characterised by two traversals of the vacuum chamber in opposite directions.

[0077] As discussed further above, because of the finite beam widths (i.e. cross-sections) of the incident and reflected beam components, a volume of intersection of the beams, V, shown schematically with a dotted ellipse in Figure 10, is formed within the vacuum chamber 350. The vacuum chamber 350 is formed in the example set-up by an anti-reflection coated glass vacuum cell with dimensions of 3 cm x 3 cm x 10 cm. The rubidium atoms in the vacuum chamber are cooled and concentrated in a cloud within the trapping volume, V. The vacuum chamber 350 is operable to provide a vacuum atmosphere through the action of a suitable vacuum pump 340, e.g. an ion pump, arranged in fluid communication with the vacuum chamber 350 via appropriate vacuum conduits 348. A vacuum valve 346 for the vacuum space is also provided. A suitable vacuum to maintain in the vacuum cell is 4 x 1 O-10mbar. The vacuum space also includes a source of atoms to be cooled, in the example setup an atom source 342 provides the rubidium atoms. The rubidium atoms are release by heating the source material, e.g. with an electrical heater element 344 that is operable to supply a DC current to heat the source material. Rubidium vapour can be provided by an alkali metal dispenser which will increase the background vapour pressure, e.g., by approximately one order of magnitude to 5 x 10-9mbar, during operation of the trap. Other forms of heating, e.g. with laser light, may also be used.

[0078] In order to characterise the behaviour of the optical trap, the number of trapped atoms, N, and their temperature, T, are measured as a function of various parameters including total beam power, P, and the level of red detuning, 5, of the cooling laser from the85Rb cooling transition. In the following, the stated values of the total beam power represent the sum of the powers of all three incident beams, which includes the powers of both cooling and repump components. As already mentioned above, the power ratio between the cooling and repump components is 3:1 and the three incident beams have equal power.

[0079] While the system will typically be designed for each beam pair to have the same power, and for the two beams of any given pair to have the same power, this is not a requirement for the system to operate successfully. It is expected that the system will be relatively tolerant to differences in beam power both between beam pairs and within a beam power, at least over a certain range of differences, e.g. a few tens of percent and perhaps up to 40%.

[0080] The parameter space to optimise according to embodiments of the invention includes variation of the following parameters: beam polarisation, beam power, level of red detuning, inclination angles and separation distances.

[0081] The effect of variation of inclination angle is now considered. An inclination angle of 45° corresponds to a conventional optical cooling geometry with three pairs of counterpropagating beams extending along mutually orthogonal axes, i.e. a Cartesian setup. Moreover, with reference to Figure 3A, it will be appreciated that an inclination angle of x = 30° is exactly equivalent to an inclination angle of x = 60°, since in both cases they deviate by ±15° from orthogonal, so by changing from x = 30° to 60° all that has happened is a 90° rotation of the tripod. We refer to inclination angle in terms of angular deviation Ax from orthogonal beams, i.e. from x = 45°. Based on previous work, an angular deviation of Ax = 25° (i.e. inclination angle, x, of 20°) is expected to be close to the boundary of the range that will function. Based on previous work, consistently good performance is expected for angular deviations in the range 10° < Ax 20°, i.e., an inclination angle range of 25° x - 40°.

[0082] It will be clear to one skilled in the art that many improvements and modifications can be made to the foregoing exemplary embodiment without departing from the scope of the present disclosure.

[0083] For those embodiments that require a repump, the repump light does not have to be introduced to co-propagate with each or every cooling beam as described above. The repump light could be added to co-propogate with only one of the cooling beams or some other subset of the cooling beams. The repump light could also be directed onto the volume of intersection along one or more beam paths that are independent of the beam paths of the cooling beams, i.e. copropagation with a cooling beam is not required.

[0084] Moreover, as explained above, while in principal embodiments, the first, second and third alignment angles form an angle of between 25° and 40° to the reference axis, more especially between 30° and 40° to the reference axis.

[0085] In the above-described embodiment a single laser has its output beam split into three components to generate the first, second and third input beams for cooling. Moreover, the first, second and third input beams are redirected back across the vacuum chamber as reflected beams by respective first, second and third mirror arrangements. However, multiple variants of this scheme are possible. For example, the the laser source may consist of three lasers, each generating one of the first to third input beams, In another variant, the reflectors could be dispensed with and the laser source could consist of six lasers, each generating one of the first to sixth beams, so that what is referred to in the above as a reflected beam is rather a beam generated by a different laser source than the beam with which it forms a counterpropagating pair.

[0086] Figures 11 to 13 are schematic drawings of variants of the first embodiment with different utilization of the laser sources. The vacuum chamber and associated components are not illustrated but will be present as shown in Figure 10. Not all the optical components are labelled, e.g. fibres, fibre couplers etc., but these will be understood from Figure 10.

[0087] Figure 11 is a schematic drawing of a first variant. In this variant, six cooling lasers 102 1 to 102 6 are provided to generate the firs to sixth cooling beams. Moreover, an optional single repump laser 202 is shown, whose output beam is combined with one of the cooling beams, namely the output from cooling laser 102 4, e.g., using a fibre coupler as illustrated. Merging repump beams into one or more of the other cooling beams is not needed but would be an option. Figure 12 is a schematic drawing of a second variant. Three cooling lasers 102 1 , 102 2, 102 3 are provided. The counter-propagating beam pairs are generated in the same way as the embodiment of Figure 10 by respective mirrors 334, 336, 338. The repump light is provided in the same way as in Figure 11 by merging the output from a repump laser 202 with the output from one of the cooling lasers; here cooling laser 102 1 .

[0088] Figure 13 is a schematic drawing of a third variant. In this variant, the cooling beam arrangement is the same as in Figure 12, but the repump beam is supplied by a free-space traverse of the vacuum chamber, labelled with reference numeral 203, that is geometrically independent of any of the cooling beams and can be at an arbitrary angle. All that is required is that the repump beam intersects with the volume of intersection V of the cooling beams.

[0089] Many further variants for generating and suitably directing the cooling beams, and the optional repump light, will be readily foreseeable to the skilled person.

[0090] REFERENCE NUMERALS

[0091] 10 mirror

[0092] 12 mirror

[0093] 14 mirror

[0094] 16 beam return subassembly

[0095] 20 polarising beam splitter (PBS)

[0096] 22 quarter-wave plate

[0097] 22’ half-wave plate

[0098] 24 half-wave plate

[0099] 26 mirror

[0100] 28 mirror

[0101] 30 mirror

[0102] 32 linear translation stage

[0103] 34 replicated lateral transfer retroreflector mirror

[0104] 100 cooling laser setup

[0105] 102 cooling laser, e.g. DFB @ 780 nm

[0106] 104 optical isolator

[0107] 106 half-wave plate

[0108] 108 polarising beam splitter (PBS)

[0109] 110 acousto-optic modulator (AOM)

[0110] 112 mirror

[0111] 114 mirror

[0112] 116 optical fibre coupler

[0113] 117 optical fibre

[0114] 118 mirror

[0115] 120 PBS

[0116] 122 vapour cell for cooling laser stabilisation

[0117] 124 PBS

[0118] 126 mirror

[0119] 128 half-wave plate

[0120] 130 mirror

[0121] 132 lens

[0122] 134 photodiode (PD)

[0123] 136 demodulation electronics

[0124] 138 mirror

[0125] 140 mirror

[0126] 142 AOM

[0127] 144 collimating lens 146 quarter-wave plate

[0128] 148 dielectric mirror

[0129] 200 repump laser setup

[0130] 202 repump laser, e.g. DFB @ 780 nm

[0131] 203 repump laser beam

[0132] 204 optical isolator

[0133] 206 half-wave plate

[0134] 208 PBS

[0135] 210 AOM

[0136] 212 mirror

[0137] 214 mirror

[0138] 216 optical fibre coupler

[0139] 217 optical fibre

[0140] 218 mirror

[0141] 220 PBS

[0142] 222 vapour cell for repump laser stabilisation

[0143] 224 PBS

[0144] 226 mirror

[0145] 228 half-wave plate

[0146] 230 mirror

[0147] 232 lens

[0148] 234 quadrupole photodiode

[0149] 238 mirror

[0150] 240 mirror

[0151] 242 AOM

[0152] 300 optical trap setup

[0153] 301 2-to-1 fibre coupler

[0154] 302 1 -to-3 fibre splitter

[0155] 304 optical fibre

[0156] 306 optical fibre

[0157] 308 optical fibre

[0158] 310 fibre coupler

[0159] 312 fibre coupler

[0160] 314 fibre coupler

[0161] 316 PBS

[0162] 318 PBS

[0163] 320 PBS

[0164] 322 quarter waveplate 324 quarter waveplate

[0165] 326 quarter waveplate

[0166] 328 quarter waveplate

[0167] 330 quarter waveplate 332 quarter waveplate

[0168] 334 mirror

[0169] 336 mirror

[0170] 338 mirror

[0171] 340 ion pump 342 atom (e.g. rubidium) source

[0172] 344 atom source heater

[0173] 346 vacuum valve

[0174] 348 vacuum conduits

[0175] 350 vacuum chamber

[0176] REFERENCES

[0177] [1] S. Sharma, B. Acharya, A. De Silva, N. Parris, B. Ramsey, K. Romans, A. Dorn, V. de Jesus, and D. Fischer, All-optical atom trap as a target for motrims-like collision experiments, Physical Review A 97, 043427 (2018). [2] US 2023 / 274849 A1 (Dragomir and Himsworth)

[0178] [3] V. Negnevitsky and L. D. Turner, Wideband laser locking to an atomic reference with modulation transfer spectroscopy, Optics express 21 , 3103 (2013).

[0179] [4] M. Aldous, J. Woods, A. Dragomir, R. Roy, and M. Himsworth, Carrier frequency modulation of an acousto-optic modulator for laser stabilisation, Optics Express 25, 12830 (2017)

[0180] [5] Jeongwon Lee, Jae Hoon Lee, Jiho Noh, and Jongchul Mun, Core-shell magneto-optical trap for alkaline-earth-metal-like atoms, Phys. Rev. A 91 , 053405.

Claims

CLAIMS1 . An optical trap (300) for trapping and cooling atoms, the optical trap comprising: a vacuum chamber (350) operable to provide a vacuum atmosphere in which atoms of an atomic species can be laser cooled via excitation of an electronic transition of the atomic species, referred to as the cooling transition; a laser source (102) configured to generate first to sixth beams of laser light of respective first to sixth beam widths and half-widths, the beams all having a frequency that is detuned below the frequency of the cooling transition; an optical arrangement (300) configured to direct the first to sixth beams to generate first, second and third counter-propagating beam pairs from the first and second, third and fourth and fifth and sixth beams respectively, such that the first, second and third beam pairs cross each other in a volume of intersection within the vacuum chamber, referred to as the trapping volume, characterised in that the first, third and fifth beams deviate from a mutually orthogonal arrangement in which they would each form an alignment angle of 45° to a reference axis, such that instead they have respective alignment angles of between 5° and 40° to the reference axis, and in that the beam axes of the first and second beams that form the first beam pair extend parallel to each other with a deviation from parallel in their mutual alignment of less than 0.1 degrees and are laterally offset from each other by a first beam pair separation distance.

2. The optical trap of claim 1 , wherein the first beam pair separation distance is such that the sum of the beam half-widths of the first and second beams is between 0.25 and 2.00 times the first beam pair separation distance in the trapping volume.

3. The optical trap of claim 2, wherein the beam axes of the third and fourth beams that form the second beam pair extend parallel to each other with a deviation from parallel in their mutual alignment of less than 0.1 degrees and have a second beam pair separation distance, and wherein the sum of the beam half-widths of the third and fourth beams is between 0.25 and 2.00 times the second beam pair separation distance in the trapping volume.

4. The optical trap of claim 3, wherein the second beam pair separation distance is such that the sum of the beam half-widths of the third and fourth beams is between 0.25 and 2.00 times the first beam pair separation distance in the trapping volume.

5. The optical trap of claim 3 or 4, wherein the beam axes of the fifth and sixth beams that form the third beam pair extend parallel to each other with a deviation from parallel in their mutual alignment of less than 0.1 degrees and have a third beam pair separation distance, andwherein the sum of the beam half-widths of the fifth and sixth beams is between 0.25 and 2.00 times the third beam pair separation distance in the trapping volume.

6. The optical trap of claim 5, wherein the third beam pair separation distance is such that the sum of the beam half-widths of the fifth and sixth beams is between 0.25 and 2.00 times the first beam pair separation distance in the trapping volume.

7. The optical trap of any of claims 1 to 6, wherein the laser source consists of one laser (102), whose output beam is split to generate the first, third and fifth beams and wherein the second, fourth and sixth beams are derived from the first, third and fifth beams respectively.

8. The optical trap of any of claims 1 to 6, wherein the laser source consists of first to third lasers (102i , 1022, 1023) to generate the first, third and fifth beams respectively and wherein the second, fourth and sixth beams are derived from the first, third and fifth beams respectively.

9. The optical trap of claim 7 or 8, wherein the second beam is derived from the first beam by arranging a first beam splitter cube (20) to receive and reflect the first beam as received after its traversal of the vacuum chamber and providing a first mirror combination (26, 28, 30) to re-route the beam reflected by the first beam splitter cube (20) to pass it again through the beam splitter cube (20) in a counter-propagating direction in relation to the first beam with a lateral offset between the beam axes of the first and second beams to provide the first beam pair separation distance (x).

10. The optical trap of claim 9, wherein the fourth beam is derived from the third beam by arranging a second beam splitter cube (20) to receive and reflect the third beam as received after its traversal of the vacuum chamber (350) and providing a second mirror combination (26, 28, 30) to re-route the beam reflected by the second beam splitter cube (20) to pass it again through the beam splitter cube (20) in a counter-propagating direction in relation to the third beam with a lateral offset between the beam axes of the third and fourth beams to provide the second beam pair separation distance (x).1 1 . The optical trap of claim 10, wherein the sixth beam is derived from the fifth beam by arranging a third beam splitter cube (20) to receive and reflect the fifth beam as received after its traversal of the vacuum chamber (350) and providing a third mirror combination (26, 28, 30) to re-route the beam reflected by the third beam splitter cube (20) to pass it again through the third beam splitter cube (20) in a counter-propagating direction in relation to the fifth beam with a lateral offset between the beam axes of the fifth and sixth beams to provide the third beam pair separation distance (x).

12. The optical trap of any of claims 1 to 6, wherein the laser source consists of first to sixth lasers (102i , 1022, 1023, 1024, 1025, 1026) to generate the first to sixth beams respectively.

13. The optical trap of claim 12, wherein the first and second lasers are arranged to provide the first beam pair separation distance, wherein the third and fourth lasers are arranged to provide the second beam pair separation distance, and wherein the fifth and sixth lasers are arranged to provide the third beam pair separation distance.

14. The optical trap of any one of the preceding claims, further comprising a first adjuster (32) that is actuatable to vary the first beam pair separation distance (x).

15. The optical trap of claim 14, further comprising a second adjuster (32) that is actuatable to vary the second beam pair separation distance (x).

16. The optical trap of claim 14, further comprising a third adjuster (32) that is actuatable to vary the third beam pair separation distance (x).

17. The optical trap of any one of the preceding claims, wherein the atomic species has a further electronic transition, referred to as the repump transition, which is required to be excited for efficient cooling to occur, and wherein the laser source (102) or a further laser source (202) is configured to generate further laser light at a further frequency tuned at the frequency of the repump transition.

18. The optical trap of claim 17, the optical arrangement further comprising a beam combiner (301 ) operable to combine the laser light and the further laser light so that each of the first to sixth beams contain both the laser light and the further laser light.

19. The optical trap of any one of the preceding claims, wherein the optical trap does not include a magnetic field generator.

20. The optical trap of any of claims 1 to 19, wherein the alignment angles are between 20° and 40°.21 . The optical trap of any of claims 1 to 19, wherein the alignment angles are between 30° and 40°.

22. The optical trap of any one of the preceding claims, wherein the first, second and third beam pairs are at least approximately equally spaced radially about the reference axis.

23. A method of laser cooling and trapping atoms, the method comprising: providing a vacuum chamber (350) operable to provide a vacuum atmosphere in which atoms of an atomic species can be laser cooled via excitation of an electronic transition of the atomic species, referred to as the cooling transition; providing laser light at a frequency detuned below the frequency of the cooling transition;providing first, second and third beams of the laser light with respective first, second and third beam widths; and directing the first, second and third beams to propagate across the vacuum chamber along respective first, second and third incident beam paths, characterised in that the first, second and third incident beam paths deviate from a mutually orthogonal arrangement in which they would each form an alignment angle of 45° to a reference axis, having instead respective alignment angles of between 5° and 40° to the reference axis, and in that the beam axes of the first and second beams that form the first beam pair extend parallel to each other with a deviation from parallel in their mutual alignment of less than 0.1 degrees and are laterally offset from each other by a first beam pair separation distance.